# Journal of the Ramanujan Mathematical Society

Volume 37, Issue 3, September 2022 pp. 273–279.

On the generating matrices of Goppa codes over hyperelliptic curves

**Authors**:
Giovanni Falcone, Agota Figula and Carolin Hannusch

**Author institution:**Department of Mathematics and Computer Science, University of Palermo, Via Archirafi, 90123 Palermo, Italy

**Summary: **
For an (imaginary) hyperelliptic curve H of genus g, we determine a basis of
the Riemann-Roch space L(D), where D is a divisor with positive degree n,
linearly equivalent to P{1} + … + P{j} + (n − j)Ω, with 0 ≤ j ≤ g, where Ω is a
Weierstrass point, taken as the point at infinity. Directly, this provides in
turn a generating matrix of a Goppa codes.

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